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14+4x(5+4x)=18
We move all terms to the left:
14+4x(5+4x)-(18)=0
We add all the numbers together, and all the variables
4x(4x+5)+14-18=0
We add all the numbers together, and all the variables
4x(4x+5)-4=0
We multiply parentheses
16x^2+20x-4=0
a = 16; b = 20; c = -4;
Δ = b2-4ac
Δ = 202-4·16·(-4)
Δ = 656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{41}}{2*16}=\frac{-20-4\sqrt{41}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{41}}{2*16}=\frac{-20+4\sqrt{41}}{32} $
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